An optimal investment strategy is “memoryless,” because it depends on present and expected future conditions, but not on the past. This article discusses the conditions required for a single, optimal investment strategy which the authors refer to as the memoryless trading rule. As a normative theory for investment decisions, memoryless trading requires an investment strategy or future course of action to describe what the trader will do when the markets achieve a given state. Memoryless trading also implies that when traders share a common utility function (which incorporates their risk preferences), wealth level, and trading orientation, there is a single, optimal investment strategy based upon market conditions. The authors show how some standard financial tools for comparing traders and measuring risk‐adjusted portfolio performance, e.g., the Sharpe ratio, violate the memoryless trading rule. They also discuss the relationship between memoryless trading and traditional equilibrium models of asset pricing.
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